Price-Linked Subsidies and Health Insurance Markups∗
Sonia Jaffe†
Mark Shepard‡
January 22, 2016
Abstract
Subsidies in the Affordable Care Act exchanges and other health insurance programs depend on prices set by insurers – as prices rise, so do subsidies. We show
that these “price-linked” subsidies incentivize higher prices, with a magnitude that
depends on the elasticity of demand and on how much insurance demand rises when
the price of uninsurance (the mandate penalty) increases. To estimate this effect, we
use two natural experiments in the Massachusetts subsidized insurance exchange. In
both cases, we find that a $1 increase in the relative monthly mandate penalty increases plan demand by about 1%. This implies that the distortion is equivalent to
the effect of a cost increase of $48 per month. A structural analysis estimates that the
price distortion is somewhat lower, about $19 per month in 2011. This distortion has
implications for the tradeoffs between price-linked and exogenous subsidies in many
public insurance programs. We propose an alternate policy that would eliminate the
distortion while maintaining some of the benefits of price-linked subsidies and discuss
how market competition and cost uncertainty affect the tradeoffs between alternative
subsidy structures.
∗
The authors would like to thank Amitabh Chandra, David Cutler, Keith Ericson, Jerry Green, Jon
Gruber, Scott Kominers, Amanda Starc, and participants of the Harvard Industrial Organization Lunch and
Harvard Health Care Policy Lunch for their helpful comments, the Lab for Economic Applications and Policy
(LEAP) at Harvard University for funds for acquiring the data, and the Massachusetts Health Connector
and its employees (especially Nicole Waickman and Marissa Woltmann) for access to and explanation of the
data. The views expressed herein are our own and do not reflect those of the Connector or its affiliates. All
mistakes are our own.
†
Becker Friedman Institute, University of Chicago, spj@uchicago.edu. Jaffe gratefully acknowledges the
support of a National Science Foundation Graduate Research Fellowship, as well as the hospitality of the
Becker Friedman Institute for Research in Economics at the University of Chicago.
‡
John F. Kennedy School of Government, Harvard University and NBER, mshepard@fas.harvard.edu.
Shepard gratefully acknowledges the support of National Institute on Aging Grant No. T32-AG000186
via the National Bureau of Economic Research, and a National Science Foundation Graduate Research
Fellowship.
1
An increasingly important model for public health insurance programs is the coverage of
enrollees through organized marketplaces offering a choice among subsidized private plans.
Long used in Medicare’s private plan option (Medicare Advantage), this model was adopted
for the Medicare drug program (Part D) in 2006 and most recently, by the Affordable Care
Act (ACA) exchanges in 2014. These programs aim to leverage the benefits of choice and
competition, while ensuring affordability through subsidies. We show that the method for
setting subsidies can affect the strength of insurer price competition, leading to an important
interaction between these two goals.
There are two basic approaches to setting subsidies. First, subsidies may be set “exogenously” – based on factors not controlled by market actors, such as an actuarial estimate
of expected cost. While exogenous subsidies create clear-cut incentives, they risk leaving
consumers with higher than expected premiums (when prices are higher than expected) or
giving them windfalls at government expense (when prices are lower than expected). To
remedy this problem, recent reforms (including Medicare Part D and the ACA) follow a
second approach: setting subsidies endogenously as a function of insurers’ prices. These
“price-linked” subsides allow the state to ensure the affordability of insurance in the face of
cost uncertainty. For instance, the ACA sets a consumer-specific subsidy so that consumers’
post-subsidy premium for the second-cheapest “silver-tier” plan equals a specified “affordable” share of their income. This ensures that at least two silver plans will be affordable,
even if prices grow faster than anticipated.
We point out an overlooked disadvantage of price-linked subsidies: they risk distorting
firms’ pricing incentives in imperfectly competitive markets. The basic intuition for the
distortion is simple: if higher prices yield higher subsidies, firms have an incentive to raise
prices. However, this intuition is only correct if higher prices increase the relative subsidies
for a firm’s plans. Since in the ACA there is a single flat subsidy,1 if it applied to all options
in the market, then (under standard assumptions) there would be no pricing distortion.
However, though the subsidy applies to all plans, it does not apply to the “outside option”
of not purchasing insurance. When the subsidy goes up, it decreases the cost of buying a
plan relative to not buying insurance. Each firm will gain some of the consumers brought
1
In other settings, subsidies vary across plans, and a plan’s subsidy is directly increasing in its own price.
These settings include Medicare Advantage – which decrease subsidies by between 30-50 cents for each $1 of
price decrease below a county benchmark – and many employers that subsidize a fixed percent (e.g., 85%) of
each plan’s premium. In these settings with “marginal” subsidies, the intuition for a price distortion is even
clearer than in the case with flat subsidies, which we focus on. Cutler and Reber (1998) show that marginal
subsidies can be advantageous to offset mispricing due to adverse selection. In theory, the distortion we
study could also mitigate adverse selection between insurance and uninsurance, but increasing the mandate
penalty would achieve the same effect without distorting the relative prices of the plans most likely to be
subsidy pivotal.
1
into the market by this price decrease; therefore, each firm has an incentive to raise the price
of any plan it thinks might affect the subsidy. This has the potential to increase government
subsidy costs, distort consumer choices, and raise prices for higher-income consumers who
do not receive subsidies.2
Our model suggests a simple alternative to remove the distortion while preserving the
affordability advantages of price-linked subsidies: apply the subsidy to the outside option as
well. While normally, the cost of not purchasing a good is fixed at zero, the ACA’s mandate
penalty for uninsurance makes such a subsidy for the outside option possible. Specifically,
if the second-cheapest silver price exceeds an expected target level, the difference would be
applied to reduce the mandate penalty (and vice versa if its price is below the target). Under
this system, subsidies would still ensure the “affordability” of at least two silver plans. But a
higher subsidy would not affect the relative prices of insurance vs. non-insurance, removing
the distortionary incentive.
Applying the subsidy to the mandate penalty effectively fixes the total subsidy to insurance – the mandate penalty plus the subsidy. So, similar to exogenous subsidies, this
structure has the (potential) disadvantage of not allowing the incentive to buy insurance to
change with prices, which might be desirable if the externality of uninsurance is linked to the
cost of health care. While exogenous subsidies tend to generate variation in consumer prices,
applying the subsidy to the mandate penalty fixes consumer prices, but generates variation
in the penalty. When markets are more competitive, the cost of endogenous subsidies is
lower, making them potentially preferable to exogenous subsidies. When the government
has precise estimates of expected costs, the benefits to endogenous subsidies are lower, pushing for exogenous subsidies or applying the subsidy to the mandate penalty. The experience
with persistently high payments through exogenous subsidies in Medicare Advantage (see
MedPAC, 2013) indicates potential political challenges to exogenous subsidies, though exogenous total subsidies could mitigate this problem by applying the subsidy to traditional
fee-for-service Medicare and including it as a bid in the market, see Section 5.
We use a simple discrete choice model of insurance plan choice to show this price distortion theoretically. We show that the pricing incentive distortion depends on the priceresponsiveness of consumers’ demand with respect to the plan’s own price and with respect
to the price of the outside option. In the case of the ACA, the main outside option is
2
If silver plan prices rise enough, the implied subsidy may exceed the price of some bronze plans, creating
a dilemma of whether to allow negative consumer premiums or to penalize the cheapest bronze plans by
capping their subsidies. The ACA does not allow negative premiums, and the phenomenon of subsidies
exceeding the prices of some plans appears to have happened widely in the bidding for 2014 plans (the first
year of exchanges). McKinsey Center for U.S. Health System Reform (2013) finds that 6-7 million uninsured
Americans will have access to a plan whose post-subsidy premium is $0. This is a substantial fraction of the
projected steady-state enrollment in exchanges of about 25 million (CBO, 2013).
2
uninsurance, whose price is the mandate penalty.3
To get an estimate of the semi-elasticity of demand with respect to the mandate penalty,
we use data from Commonwealth Care (CommCare), the pre-ACA subsidized insurance
exchange in Massachusetts. A key model for the ACA exchanges, CommCare offered subsidized non-group insurance for eligible individuals earning less than 300% of poverty.4 We
use administrative data on plan bids and prices and consumer demographics, plan choices,
and healthcare costs for all CommCare enrollees from the start of the program in November
2006 until June 2011. We supplement this with data on the uninsured from the American
Community Survey. While this is related to past work estimating the price-elasticity of of
insurance demand when the price of the outside option is fixed (e.g. Gruber and Poterba
(1994) on non-group insurance for the self-employed and Gruber and Washington (2005) on
employer-sponsored insurance), there are no similar estimates of the response of coverage
to the mandate penalty in a low-income exchange setting. The closest related work is that
of Chandra et al. (2011), however, their focus is on the effect of the mandate penalty on
adverse selection, so they do not report estimates of the increase in total coverage.
We use variation from two natural experiments that occurred in 2007-2008 to estimate
the responsiveness of demand to the mandate penalty. The first is the introduction of the
mandate penalty in December 2007 for individuals earning above 150% of poverty. With
poorer enrollees as the control group, (and other years for a triple difference) we find that
the number of new enrollees in the cheapest plan exceeded trend by about 23% of its steadystate size. The second experiment uses a decrease in all plans’ premiums for consumers
100-150% poverty in July 2007. Because a lower price of all inside options has an equal
effect on relative prices as a higher price of the outside option, this experiment can be used
to estimate the response of insurance demand to the relative mandate penalty. Again using
a triple-difference regression, we find new enrollment in the cheapest plan grew by 17% of
steady-state size. Scaling each of these changes by the corresponding change in the mandate
penalty amounts (which varied by income), we find that on average each $1 increase in the
monthly penalty increased enrollment by 0.95%.
The distortion also depends on the own-price semi-elasticity of demand. We first adapt
3
Other sources of insurance are unlikely to be an option for the ACA’s subsidy-eligible population.
Anyone eligible for “affordable” employer-sponsored insurance (with a premium less than 9.5% of income) is
not eligible for exchange subsidies, and a similar provision applied in Massachusetts during our study period.
Non-group insurance purchased outside of exchanges is likely to be a dominated choice relative to the heavily
subsidized exchange plans.
4
Prior to 2014, CommCare was separate from Massachusetts’ unsubsidized exchange for individuals above
300% poverty, which has been studied by Ericson and Starc (2012). Under the ACA, the two Massachusetts
exchange populations merged together, and most individuals below 100% poverty are shifting to Medicaid
(with the exception of some legal immigrants remaining in the exchange). Individuals earning less than 400%
of poverty receive subsidies, while those above 400% poverty can purchase the same plans without subsidies.
3
the Chan and Gruber (2010) estimates for this same market to allow for out-of-market
substitution. Their coefficient implies that each $1 premium increase reduces demand for
the cheapest plan among new enrollees by 1.97%. Combined with the .94% semi-elasticity
with respect to the mandate penalty, this implies that having endogenous subsidies had the
same effect on prices as a cost increase for the cheapest plan of $48 per member per month.
That is 16% of the average monthly health care costs incurred by CommCare consumers in
the 2008 plan year ($308).
To convert this to a price increase and more formally consider alternative subsidy policies,
we then estimate a structural model of the market. We estimate demand parameters using
generalized method of moments. The natural experiments permit us to estimate the variance
in unobserved heterogeneity in the value of insurance in addition to observed heterogeneity
in price sensitivity and plan values. We find price semi-elasticities that are substantially
higher than those in Chan and Gruber (2010), averaging 2.63% in 2008. We also estimate
firm and consumer cost parameters to be able to calculate firms’ first order conditions under
alternative subsidy rules. We find that switching from the existing subsidy rule to exogenous
subsidies (set at the level of the equilibrium endogenous subsidy) lowers prices by about $20.
The ACA exchanges differ from Massachusetts CommCare in a variety of ways. The
medical loss ratios and the inclusion of some unsubsidized consumers may mitigate the
distortion. Conversely, the multi-plan insurers and high concentration in many markets
(see Abelson et al., 2013) are likely to exacerbate it. The distortion is also relevant in
other markets where firms have market power and there is meaningful substitution between
the in-market plans and the outside option. Medicare Advantage, Medicare Part D, and
employer-sponsored plan choices all subsidize insurance in a form of exchange and have
to determine subsidy levels. Although estimating the distortion in these other markets is
beyond the scope of this paper, our theory suggests that it will be relevant We discuss the
implications for other markets in Section 5.
We are not aware of past research that has analyzed the distortion we discuss. The closest
related work is Decarolis (2013), which highlights a different pricing distortion in Medicare
Part D. By increasing its plan prices for higher-income enrollees, insurers can increase their
payments for low-income subsidy recipients, who do not pay prices. However the structure in
Part D is different, creating different and often more subtle incentives to game the systems.
Also, the subsidized consumer share of the Part D market (about 40%) is substantially
smaller than their share in the ACA exchanges (about 80%).
The remainder of the paper is structured as follows. Section 1 sets up a standard choice
model and derives a reduced-form formula for the distortion in the markup due to the
endogeneity of the subsidy. It proposes an alternative policy that eliminates this distortion
4
while maintaining price-linked subsidies. Section 2 describes the data we use from the
Massachusetts Connector. Section 3 uses two natural experiments in this market to to
calibrate the relevant semi-elasticity of demand with respect to the mandate penalty and
combines this estimate with the estimate from Chan and Gruber (2010) of the sensitivity
of demand to own price to get a quantitative estimate for the distortion in the markup
due to endogenous subsidies. Section 4 does a structural estimation of demand and cost
in the market and considers the effects of counterfactual subsidy policies on prices and
quantities Section 5 discusses the broader relevance of our findings for the ACA and other
insurance markets; it then lays out the tradeoffs between different subsidy structures and
the circumstances that tend to favor one over the other. Section 6 concludes.
1
Theory
We adapt a standard discrete choice model of demand to allow for endogenous subsidies.
We use the necessary first-order conditions for Nash equilibrium to derive sufficient statistics
that capture the effect of subsidy rules on insurers’ optimal prices. We focus on the case
relevant to our data from the Massachusetts Connector, where each insurer offers only 1
plan. We workout the multi-plan insurer case in the Appendix and discuss how it might
differ from our baseline in Section 5.
Insurers j = 1 · · · J offer differentiated products and compete by setting prices {Pj }j=1···J .
The exchange collects price bids and uses them to determine the subsidy S(P ) based on a
formula that insurers know before bidding. Subsidy-eligible consumers then choose which (if
any) plan to purchase based on plan attributes and post-subsidy prices Pjcons = Pj − S(P ).
If they choose not to purchase a plan, they are subject to the legally applicable mandate
penalty, M . Consumer demand for plan j, Qj (P cons , M ), is a function of all premiums and
the mandate penalty. As in most discrete choice models, we assume that utility is (locally)
quasi-linear in price, so consumers only care about prices relative to other prices and to
mandate penalty.
We assume that insurers set prices simultaneously to maximize static profits, knowing
the effects of these choices on demand and cost.5 As in most recent work on insurance
(e.g. Einav et al. (2013)), we assume that plan attributes are held fixed, focusing instead
on the effect of subsidies on pricing conditional on plan attributes.6 We assume constant
5
We therefore abstract from pricing dynamics or incomplete information. As noted below, uncertainty
would spread the distortion out across multiple plans, but would not eliminate it.
6
This assumption is less problematic in the insurance industry, where many attributes are severely constrained by regulation. For instance, in the Massachusetts exchange we study empirically, the regulator
specifies the services insurers must cover and all of the associated co-payments.
5
marginal cost and we abstract from adverse selection by assuming ideal risk adjustment; we
can therefore specify a constant per-enrollee marginal cost cj for insurer j.7
The insurer profit function is:
πj = (Pj − cj ) · Qj (P cons , M ) .
The necessary conditions for Nash equilibrium are that each firm’s first-order condition is
satisfied: 8
dQj
dπj
= Qj (P cons , M ) + (Pj − cj ) ·
= 0.
dPj
dPj
(1)
This differs from standard oligopoly pricing conditions in two respects. Because of the
subsidies, the firm’s price Pj enters consumer demand indirectly, through the subsidized
premiums, P cons . Also, the term dQj /dPj is not the slope of the demand curve, but a
composite term that combines the slope of demand and the effect on demand via the effect
of the price on the subsidy and mandate penalty. The total effect of the premium on demand
is:
!
X ∂Qj
dQj
∂Qj
∂Qj ∂M
∂S
=
+
,
(2)
−
cons
cons
dPj
∂Pj
∂P
∂P
∂M
∂P
j
j
k
k
which depends on the specific policy for determining subsidies and the mandate penalty.
1.1
Pricing Distortion
To see the effect of the subsidy policy, we compare firms’ first-order conditions under exogenous and endogenous subsidies.
7
Risk adjustment works by adjusting the payment insurers receive to be higher than Pj for sick, high-cost
enrollees and lower for healthy enrollees. In ideal risk adjustment, the quantity (Pij − cij ) is constant across
enrollees, allowing us to write it in the standard form (Pj − cj ). Both the Massachusetts and ACA exchanges
include sophisticated (though likely still imperfect) risk adjustment. Nonetheless, the effects we identify all
carry over to a model with adverse selection, with more complicated formulas for the sufficient statistics.
8
These first-order conditions would be necessary conditions for Nash equilibrium even in a more complicated model in which insurers simultaneously chose a set of non-price characteristics like copays and provider
network. Thus, the theoretical point we make about price-linked subsidies holds when quality is endogenous,
though there may also be effects on quality and cost levels, which we don’t capture.
6
Exogenous Subsidies
Exchanges could set flat, exogenous (i.e., based on factors not controlled by market actors)
subsidies and mandate penalties.
Exogenous Subsidy: Pjcons = Pj − S,
∂M
∂S
=
=0
with
∂Pj
∂Pj
∀j.
As a result of subsidies and the mandate penalty being unaffected by any plan’s price,
dQj /dPj in Equation (2) simplifies to the demand slope ∂Qj /∂Pjcons . Even though there are
subsidies, the equilibrium pricing conditions are not altered relative to the standard form for
differentiated product Bertrand competition. Under this exogenous subsidies benchmark,
firms set markups as:
M kupEx
j ≡ P j − cj =
1
ηj
∀j,
∂Q
j
where ηj ≡ − Q1j ∂P cons
is the own-price semi-elasticity of demand.
j
Price-Linked Subsidies
Alternatively, exchanges could link subsidies to prices (but again set M exogenously). This
is the approach taken in Massachusetts and the ACA exchanges. A key advantage of this
approach is that a state can ensure affordability to consumers even if prices are higher
than expected and avoid windfalls to consumers when prices are lower than expected. This
transfer of health care cost risk from individuals to the state is a key motivation for pricelinked subsidies.
However, linking subsidies to prices distorts insurers’ pricing incentives. To see this
distortion, consider a subsidy rule (similar to that used in Massachusetts) that sets S(P )
so that the post-subsidy premium for the cheapest plan equals a pre-determined “affordable
amount” (based on income). With this policy, the subsidy rises with the price of the cheapest
plan, but the mandate penalty is still exogenous to plan prices. Formally, the subsidy for a
given income group would be set so that:
Subsidy Linked to Min Price: S (P ) = min Pj − AffAmt
j
=⇒
7
∂S (P )
= 1,
∂Pj
∂M
= 0 ∀j,
∂Pj
(3)
where j is the index of the cheapest plan. For example, in 2007, the affordable amount for a
consumer earning between 150-200% of poverty was $40 per month, and the cheapest plan
in the “Outside of Boston” region bid a price of $295.84 per month. As a result, the subsidy
for this income group was set at $255.84.9
This price-subsidy link changes optimal pricing for an insurer that believes it will have
the cheapest plan. Raising this plan’s price by $1 does not affect its own consumer premium
(which is offset by the higher subsidy) but lowers the premium of all other plans by $1.
Initially, this may sound the same as the standard case – raising own price by $1 affects
demand identically to lowering all other options’ prices by $1. But critically, the price
increase for the cheapest plan does not lower the price of being uninsured, (i.e. the mandate
penalty) and therefore does not affect the relative price of the plan compared to uninsurance.
This creates an extra incentive for the cheapest plan to markup its price, which in turn
increases subsidy costs to the state.
To see the distortion analytically, consider how the endogenous subsidy affects the total
derivative of demand with respect to price for the cheapest plan:
dQj
dPj
=
∂Qj
∂Pjcons
−
!
X ∂Qj
k
∂Pkcons
∂Qj
X ∂Qj ·1+
·0=
− cons .
∂M
∂Pk
k6=j
Since the affordable amount is fixed, raising Pj is equivalent to lowering consumer premiums
for all other plans. Next, we use the fact that with utility linear in price, raising the prices of
P ∂Qj
∂Q
all options (including uninsurance) equally does not affect demand, that is k ∂P cons
+ ∂Mj =
k
0 ∀j. Combining these two equations implies that
dQj
dPj
=
∂Qj
∂Pjcons
+
∂Qj
∂M
.
(4)
However, if the firm raises its price so much that it is no longer the cheapest plan, then it is
dQj
∂Qj
no longer pivotal for the subsidy, and dPj = ∂P cons .
j
Plugging Equation (4) into Equation (1) and rearranging yields the following markup
condition for the cheapest plan when subsidies are endogenous
M kupEnd
≡ Pj − cj =
j
9
1
,
ηj − ηj,M
In later years in the Massachusetts exchange, there were “incremental” subsidies to pricing higher, so
more expensive plans received larger subsidies. We do not model this feature of the subsidy scheme, which
will not be replicated in the ACA and was only present for enrollees earning less than 150% poverty during
the 2007-08 period we study.
8
where ηj,M =
1 ∂Qj
Qj ∂M
is the semi-elasticity of demand with respect to the mandate penalty.
Distortion
Price-linked subsidies lower the effective price sensitivity faced by the cheapest plan, leading
to a higher equilibrium markup than under exogenous subsidies. In our model without
uncertainty, this distortion only applies to the cheapest plan, though there may be strategic
responses by other firms.10 If the distortion is large enough that the cheapest plan would
want to price above the second cheapest plan, it instead sets a price equal to the second
cheapest plan.
If the semi-elasticities of demand are constant across the relevant range of prices (owncost pass-through equals 1), the increase in markup for the cheapest plan is:
− M kupEx
M kupEnd
j =
j
ηj,M
ηj ηj − ηj,M
,
(5)
though the distortion cannot cause the cheapest plan to raise its price above that of the
second cheapest plan. Constant semi-elasticities may be a good approximation in some
markets; alternatively, the estimated increase in markups can be thought of as an estimate
of how much marginal costs would have had to decrease to offset the incentive distortion
generated by endogenous subsidies.11
The distortion will tend to be larger when markets are less competitive. When there
are fewer firms, on average we expect ηj to be smaller because consumers have fewer other
options and ηj,M to be higher because a given firm will get a larger share of however many
consumers enter the market when the penalty goes up. Both of these effects increase the
distortion. Also, with fewer firms, it is less likely that the second cheapest plan will be close
in price to the cheapest plan and thereby act as an effective cap on the distortion.
This pricing distortion can have an important effect on social welfare. While the price
distortion is on the cheapest plan, it also drives up the subsidy, which raises the government’s
costs for all enrolled individuals, not just those that chose the cheapest plan. With a marginal
10
Like much of the related literature, we make the simplifying assumption that firms know what equilibrium
they are in, so there is no uncertainty about which plan will be cheapest. In a more realistic model with
uncertainty about others’ prices (perhaps due to uncertainty about others’ costs) then the distortionary
term ηj,M would be weighted by the probability of being the lowest price plan. The (ex-post) cheapest
plan would have a smaller distortion, but there would also be distortions to other plans’ prices. Strategic
complementarity in prices could further exacerbate these.
11
This is similar to the idea from Werden (1996) that, without assumptions about elasticities away from
the equilibrium, one can calculate the marginal cost efficiencies needed to offset the price-increase incentives
of a merger.
9
cost of government funds above one, this transfer from the state to insurers is socially costly.12
1.2
Price-Linked Subsidies Without the Distortion
Our model suggests a simple alternative to exogenous subsidies that would fully correct
the distortion while keeping price-linked subsidies: apply the same subsidy to the mandate
penalty. Specifically, set an exogenous base mandate penalty amount M0 and reduce this by
the subsidy, for a final penalty of
M = M0 − S (P ) .
The base amount could be set so that, based on the government’s expectations about prices,
the final penalty would be similar to the penalty specified by current law.13 This adjustment
would remove the pricing distortions discussed above. If the cheapest plan raised its price
bid by $1, this would leave its premium unaffected (since the subsidy would rise) but lower
by $1 the price of all other plans and the cost of uninsurance. The effect on own demand
would be
∂Qj
∂Qj
∂Qj
dQj X
=
=
− cons −
dPj
∂Pk
∂M
∂Pjcons
k6=j
The price has only its direct effect on the demand for each plan, so even if insurers offer
multiple plans (the ACA case), the subsidy does not distort incentives. Therefore, optimal
prices would be identical to the benchmark case with exogenous subsidies. We simulate the
market under this policy in Section 4.3 and discuss the tradeoffs in Section 5.
2
Data
While the theory of the distortion from price-linked subsidies is clear, the question remains
whether the distortion is large enough to be of practical importance. To estimate the size
of the distortion, we turn to data from the Massachusetts subsidized health insurance exchange (called Commonwealth Care, or “CommCare”). Created in the Massachusetts’s 2006
health reform, CommCare facilitates and subsidizes private insurance coverage for individuals earning less than 300% of poverty and without access to insurance through an employer
12
In addition, the price distortion affects relative premiums and changes the allocation of consumers across
plans. But because relative prices may not equal relative marginal costs with imperfect competition (they
differ by the difference in markups), it is not clear whether this has a positive or negative effect.
13
In particular, policy makers would want to increase M0 over time with their estimate of medical cost
growth, to avoid having the mandate penalty decline as costs and therefore prices and subsidies increase.
10
or another government program. The market is quite concentrated, with just four insurers
offering plans during the period we study, making it an appropriate setting to study imperfect competition. Importantly, there have been several changes in plan premiums and the
mandate penalty over time, allowing us to identify the relevant demand elasticities.
We use administrative data on plan choices, consumer demographics, and realized costs
for all enrollees in the CommCare program from 2006 through June 2011.14 For each month,
we observe the set of participating members, their demographics, their available plans and
premiums, the plan they chose and their realized costs while enrolled. Our main analysis
focuses on trends in the number of consumers entering the market (“new enrollees”). Every
month, some individuals become newly eligible for CommCare, for instance due to job loss
or other income changes. These individuals then choose whether to enroll and which plan
to sign up for if they enroll. Since enrollees seldom switch plans, we focus on the choices
of these new enrollees, instead of existing enrollees. As a robustness check, we adjust firms’
first-order conditions for the fact that once an enrollee choses a plan, they will likely stick
with it.15
Table 1 shows summary statistics for our sample. The data include 490,368 unique
consumers. The population is quite poor, with over half having family income less than
the poverty line. There were an average of 11,365 new enrollments per month, giving us
a substantial sample to study changes over time in this statistic. Since consumers below
poverty do not pay premiums (all plans cost $0) or a mandate penalty, they act as a control
group for our analysis of the population between 100-300% of poverty.
3
Reduced-form Estimation
Recall that in the case of single-plan insurers, our formula for the increase in markups is:
− M kupEx
M kupEnd
j =
j
ηj,M
ηj ηj − ηj,M
.
An estimate of the own price elasticity, ηj , is available in the literature (see Section 3.3), so
we focus on estimating ηj,M , the effect on demand for the cheapest plan when the mandate
14
This data was obtained under a data use agreement with the Massachusetts Health Connector, the
agency that runs CommCare.
15
In theory, price changes could also affect the number of consumers exiting the market, meaning our
estimates would understate the true elasticities. However, studying exits was complicated by an income
verification program introduced around the same time as our other reforms (late 2007 and early 2008). This
forced many enrollees to leave the market, leading to substantial noise and potentially bias in an analysis of
exits. Thus, we chose to focus only on new enrollments.
11
Table 1: Summary Statistics
Full
Sample
<100
100-150
150-200
200-250
250-300
Enrollment
Total Unique
Enrollees
490,368
267,642
95,567
72,657
35,966
18,536
Monthly
Enrollment
141,803
[43,968]
72,728
[16,922]
31,173
[10,596]
23,250
[7,741]
12,225
[4,457]
6,338
[2,375]
Monthly New
Enrollees
11,365
[3,525]
6,031
[2,587]
2,346
[1,773]
1,863
[635]
942
[324]
485
[162]
Enrollment Spell
Length (months)
Share of Enroll.
Months
14.5
[12.0]
14.1
[11.6]
15.2
[12.3]
14.6
[12.7]
14.6
[12.6]
14.8
[12.5]
100.0%
51.3%
20.8%
15.5%
8.2%
4.2%
$390.22
[$85.31]
$385.54
[$83.23]
$384.18
[$82.13]
$392.59
[$76.95]
$415.22
[$101.90]
$419.71
[$102.89]
$22.28
$0.00
$4.90
$48.72
$96.30
$137.83
$8.66
[$15.25]
$0.00
[$0.00]
$0.00
[$0.00]
$18.01
[$0.88]
$36.37
[$1.49]
$54.78
[$2.99]
39.9
[14.2]
37.0
[14.2]
41.4
[14.1]
43.7
[13.1]
44.7
[12.9]
45.7
[12.7]
47.2%
52.2%
42.0%
40.8%
42.9%
44.4%
Monthly Prices
Insurer Price Bid
Consumer
Premium
Mandate Penalty
(starting Jan 2008)
Demographics
Age
Male
Income Group (% of Federal Poverty Line)
NOTE: This table shows means and standard deviations (in brackets) of statistics about CommCare
enrollees from November 2006 to June 2011. “Insurer Price Bid” shows the enrollment-weighted average
price paid to firms for an enrollee. Premiums are the average (enrollment-weighted) post-subsidy monthly
prices consumers pay for plans. The mandate penalty – which is set by law as half of each income group’s
affordable amount – is its average monthly value from January 2008 (the month the regular penalty started)
until June 2011.
penalty is raised. In what follows, we use two natural experiments in CommCare to estimate
this key statistic. Some details of the analysis of these natural experiments and robustness
checks are left to the Appendix B.
12
3.1
Mandate Penalty Introduction Experiment
Our first strategy uses the mandate penalty’s introduction. Under the Massachusetts health
reform, a requirement to obtain insurance took effect in July 2007. However, through November 2007 the requirement was not enforced by any financial penalties. Financial penalties
began in December 2007. Those earning more than 150% of poverty who were uninsured in
December forfeited their 2007 personal exemption on state taxes. Starting in January 2008,
the mandate penalty was assessed based on monthly uninsurance. The monthly penalties
depended on income, ranging from $17.50 for a person with household income of 150-200%
of poverty to $52.50 for someone between 250-300% of poverty.
There was a spike in new enrollees into CommCare for people above 150% of poverty
(the group actually subject to the penalties) exactly concurrent to the introduction of the
financial penalties in December 2007 and early 2008. Figure 1 shows this enrollment spike
for the cheapest plan, which is proportional to the overall spike; (a fairly constant 60%
share of new enrollees chose the cheapest plan.) To make magnitudes comparable for income
groups of different size, the figure shows new enrollments as a share of the same plan’s total
enrollment in that income group in June 2008.16
We believe that this enrollment spike was caused by the financial penalties for three
reasons. First, there were no changes in plan prices or other obvious demand factors for
people above 150% of poverty that occurred at the same time. Second, as Figure 1 shows,
there was no concurrent spike for people earning less than poverty (who were not subject to
the penalties),17 and there was no enrollment spike for individuals above 150% of poverty in
December-March of years other than 2007-08. Finally, Chandra et al. (2011) show evidence
that the new enrollees after the penalties were differentially likely to be healthy, consistent
with the expected effect of a mandate penalty in reducing adverse selection.
We estimate the semi-elasticity associated with this response using a triple-differences
specification, analogous to the graph in Figure 1. Table 2 shows the coefficients on for each
treatment month (December 2007 through March 200818 ) for each group by 50% of poverty
16
We use June 2008 as a baseline because enrollment, which had been steadily growing since the start
of CommCare, stabilizes around June 2008. Therefore, we treat June 2008 enrollment as an estimate of
equilibrium market size.
17
People earning 100-150% of poverty are omitted from this analysis because a large auto-enrollment took
place for this group in December 2007, creating a huge spike in new enrollment. But the spike occurred
only in December and was completely gone by January, unlike the pattern for the 150-300% poverty groups.
This auto-enrollment did not apply to individuals above 150% of poverty (Commonwealth Care (2008)) so
it cannot explain the patterns shown in Figure 1.
18
The application process for the market takes some time, so people who decided to sign up in January
may not have enrolled until March and the mandate rules exempted from penalties individuals with three
or fewer months of uninsurance during the year.However most of the effect is in December and January, so
focusing on those months does not substantially affect our estimates.
13
.2
Share of June 2008 Enrollment
.05
.1
.15
0
June2007
Dec2007
150−300% Poverty (2007−08)
150−300% Pov. (Other Years)
June2008
Dec2008
<100% Pov. (2007−08)
Figure 1: New Enrollees in Cheapest Plan by Month
NOTE: This figure shows for two income groups the monthly number of new enrollees into CommCare’s
cheapest plan as a share of total June 2008 enrollment. The vertical line is drawn just before the introduction
of the mandate penalty, which applied to people 150-300% poverty but not those below 100% poverty. The
“150-300% Poverty (Other Years)” series shows average new enrollments in each calendar month in all years
in our data except July 2007–June 2008. Each income group’s numbers are normalized by the group’s total
enrollment (in the same plan) in June 2008, so units can be interpreted as fractional changes in enrollment.
“New enrollments” include both individuals enrolling in CommCare for the first time and individuals reenrolling after a break in coverage, since both groups select a new plan. For the 150-300% poverty group,
the cheapest plan is defined as the lowest-premium plan (or plans if there is a tie) in each individual’s
choice set.For the below 100% poverty group for whom all plans are free, the cheapest plan is defined as the
lowest-premium plan for 150-200% poverty enrollees in the same region.
interval (the narrowest we have). The regressions also include group dummies, dummies
for the treatment months, and dummies for the treatment months in other years to get the
triple difference.19 The coefficients are a little larger for the higher income groups – about
25% instead of 21% – who faced higher mandate penalties. Given the mandate penalties
of $17.50-$52.50, the coefficients imply that each $1 increase in the mandate penalty raised
demand by between 1.2% for the 150-200% of poverty group to 0.48% for the 250-300% of
19
There are also CommCare-year dummy variables and fifth-order time polynomials, separately for the
treatment and control group, to control for underlying enrollment trends. (The CommCare-year starts in
July, so these dummies will not conflict with the treatment months of December to March.)
14
Table 2: Introduction of the Mandate Penalty
Effect on New Enrollees in Cheapest Plan June 2008 Enrollment
Income Group (% of Poverty Line)
Income group x Dec2007
x Jan2008
x Feb2008
x Mar2008
Total
Observations
R-Squared
150-200%
200-250%
250-300%
0.101***
(0.007)
0.061***
(0.007)
0.026***
(0.007)
0.020**
(0.008)
0.113***
(0.007)
0.085***
(0.007)
0.045***
(0.006)
0.020***
(0.006)
0.091***
(0.008)
0.086***
(0.007)
0.051***
(0.006)
0.022***
(0.007)
0.208***
(0.026)
0.263***
(0.022)
0.250***
(0.024)
102
0.927
102
0.922
102
0.920
Robust s.e. in parentheses; *** p < 0.01, **p < 0.05, *p < 0.1
NOTE: This table performs the triple-difference regressions analogous to Figure 1. The dependent variable
is the number of new CommCare enrollees who choose the cheapest plan in each month in an income group,
scaled by total group enrollment in that plan in June 2008. There is one observation per income group
(increments of 50% poverty for the treatment groups, plus the <100% poverty control group) and month (from
April 2007 to June 2011). There are CommCare-year dummy variables and fifth-order time polynomials,
separately for the treatment and control group, to control for underlying enrollment trends. (The CommCareyear starts in July, so these dummies will not conflict with the treatment months of December to March.)
There are also dummy variables for all calendar months of December-March for the treatment group, to
perform the triple-difference. See the note to Figure 1 for the definition of new enrollees and the cheapest
plan.
poverty group, with a weighted average of 0.97%.
3.2
Affordable Amount Decrease Experiment
Our second strategy for identifying the effect of the price of the outside option on the
cheapest plan’s demand uses changes in the “affordable amount.” Recall that CommCare
sets subsidies so that the post-subsidy premium for the cheapest plan equals the affordable
amount. Therefore, in our model for a fixed set of pre-subsidy prices, a $1 decrease in the
affordable amount has an equivalent effect as a $1 increase in the mandate penalty.
This approach addresses a concern with our first method: that the introduction of a
15
0
Share of June 2008 Enrollment
.04
.08
.12
.16
mandate penalty may have a larger effect (per dollar of penalty) than a marginal increase in
penalties. It also allows us to obtain estimates for the 100-150% poverty group, who faced a
$0 mandate penalty.
Mar2007
July2007
Jan2008
100−150% Poverty (2007−08)
100−150% Pov. (Other Years)
July2008
Jan09
200−300% Pov. (2007−08)
Figure 2: New Enrollees in Cheapest Plan by Month, around the Change in the Affordable
Amount
NOTE: This figure shows for two income groups the monthly number of new enrollees into CommCare who
chose the cheapest plan, scaled by total group enrollment in that plan in June 2008. The vertical line is
drawn just before the decrease in the affordable amount (the consumer premium for the cheapest plan) from
$18 to $0 for the 100-150% poverty group. During this period, the affordable amounts for the 200-300%
poverty groups were essentially unchanged.The “100-150% Poverty (Other Years)” series shows average new
enrollments in the corresponding calendar month in all other years in our data after June 2008. We exclude
December 2007 for the 100-150% poverty group because a one-time auto-enrollment caused a sharp spike in
new enrollees (to over 30% of June 2008 enrollment), and showing this point makes it difficult to see the
other points in the graph. See the note to Figure 1 for the definition of new enrollees and the cheapest plan.
The most significant changes in the affordable amount occurred in July 2007 for consumers between 100-150% of poverty, when the affordable amount fell from $18 to $0.20
20
Prices in CommCare usually change in July, but in the first year of the program, prices were held fixed
from November 2006 to June 2008, so firms’ price-bids did not change at the same time as this change in the
affordable amount. CommCare did simultaneously eliminated premiums for this group, so all plans became
free (the premium of all plans – previously up to $56.22 more than the cheapest plan – were differentially
lowered to equal the cheapest premium – now $0). This change should unambiguously lower enrollment in
what was the cheapest plan, since the relative prices of all other plans fall. So our estimate will be a lower
16
Table 3: Decrease in the Affordable Amount.
Effect on New Enrollees in Cheapest Plan / June 2008 Enrollment
100-150% Poverty x
Month
Observations
R-Squared
July 2007
Aug 2007
Sep 2007
Oct 2007
Total
0.063***
(0.008)
0.035***
(0.009)
0.016*
(0.008)
0.055
(0.008)
0.169**
(0.032)
104
0.958
Robust s.e. in parentheses; *** p < 0.01, **p < 0.05, *p < 0.1
NOTE: This table reports the triple-difference coefficients from a regression analogous to Figure 2. The
dependent variable is the number of new CommCare enrollees in the cheapest plan, scaled by total group
enrollment in that plan in June 2008. There is one observation per income group (the 100-150% poverty
treatment group, and the 200-300% poverty control group) and month (from March 2007 to June 2011).
There are CommCare-year dummy variables and fifth-order time polynomials, separately for the treatment
and control group, to control for underlying enrollment trends. (The first CommCare year ends in June
2008, so there is no conflict between the CommCare-year dummies and the treatment months of July to
October 2007.) A dummy for the treatment group and dummy variables for all calendar months of JulyOctober for the treatment group, give the triple-difference. Dummy variables are also included to control
for two unrelated enrollment changes: (a) for 100-150% poverty in December 2007, when there was a large
auto-enrollment spike, and (b) for 200-300% poverty in each month from December 2007 to March 2008,
when there was a spike due to the introduction of the mandate penalty. See the note to Figure 1 for the
definition of new enrollees and the cheapest plan.
As a control group, we use the 200-300% poverty group, whose affordable amounts were
essentially unchanged in July 2007. Figure 2 shows normalized monthly new enrollments in
the cheapest plan. Though the series are noisy there is a clear jump in the new enrollment
for the 100-150% of poverty group in July 2007 and subsequent months relative to control
groups.21
Table 3 presents the regression results corresponding to Figure 2. The decrease in the
affordable amount increased enrollment in the cheapest plan by 16.9% points, implying a
0.94% effect for each $1 decrease in the affordable amount. This semi-elasticity is very similar
the one we estimated from the mandate penalty introduction.
3.3
Pricing Distortion Approximation
Table 4 combines the coefficients estimated above with the corresponding changes in the
mandate penalty to get the semi-elasticity with respect to the mandate penalty for each
income group and for the market overall. The semi-elasticities are generally decreasing in
income, as one would expect. The exception is the semi-elasticity for 100-150% poverty
bound on the effect of just lowering the affordable amount (the effect we want to estimate).
21
The large spike in 200-300% poverty enrollment in December 2007 reflects the mandate penalty introduction, which we used for our first identification strategy.
17
(0.0094), but we consider that estimate to be a lower bound because of the other price
changes that happened at the same time (see footnote 20). On average $1 increase in the
monthly mandate penalty increases overall enrollment in the cheapest plan by 0.95%.
Table 4: Estimated Semi-Elasticities
Income Group (% of Poverty)
Subsidy
Change
Mandate Penalty Introduction
100-150%
150-200%
200-250%
250-300%
Enrollment % Increase
Dollar Change
16.9%
$18.00
20.8%
$17.50
26.3%
$35.00
25.0%
$52.50
Mandate Semi-Elasticity
Enrollment Shares
0.94%
46.1%
1.19%
31.3%
0.75%
15.1%
0.48%
7.5%
Market Average
0.95%
NOTE: This table weights the estimated semi-elasticities for different groups by June 2008 enrollment shares
to get one overall “mandate semi-elasticity.”
We adjust Chan and Gruber (2010)’s semi-elasticity of demand to allow for out of market
substitution22 and get
ηj,M
ηj ηj − ηj,M
=
0.0095
≈ $48.
0.0197(0.0197 − 0.0095)
(6)
Suggesting that having endogenous subsidies is equivalent to a $48 cost increase for the
cheapest plan. This is substantial: it is 16% of the average health care costs of enrollees in
the 2008 plan year ($308).
In a reduced form context, we need to assume constant semi-elasticities to interpret this
as a price change. (Or equivalently, an own pass-through rate of 1 and a cross pass-through
rate of zero.) If semi-elasticities are not constant in own price, or there is substantial price
response from the other plans this will not be a good estimate of the change in price due to
the incentive distortion. Therefore we use our estimates of the semi-elasticity of demand with
22
For new enrollees, they find a price coefficient of -0.027. The uninsured numbers from American Community Survey and the CommCare enrollment tell us that 57% of the eligible market buys insurance; combined
with an in-market share of 47.3%, the cheapest plan has an overall market share of 27%. The logit model
implies an own-price semi-elasticity of
ηj = −α · (1 − Qj ) = 0.027 · (1 − 0.27) = 0.0197.
Note that allowing for out-of-market substitution mechanically makes this elasticity larger than the .0154
reported by Chan and Gruber (2010); the estimated distortion would be larger if we used their number.
18
respect to the mandate penalty generated by these natural experiments to help calibrate a
structural model to estimate the equilibrium price effect of endogenous subsidies.
4
Structural Estimation **PRELIMINARY**
To get a fuller picture of the market and consider the effects of alternative subsidy structures,
we turn to a structural model. We estimate a static model where plans set plan premiums,
consumers choose plans, and then consumers incur health care costs.
4.1
Demand
Each consumer i is characterized by observable attributes Zi = {ri , ti , yi , di }: r refers to the
region they live in, t to the time period (year) they make their choice, y is income, and d
is the demographic, which is gender crossed with 5 year age bins. We drop the i subscript
when the characteristic itself is a subscript, e.g. Myi = My Each plan sets one price Pj , and
the premiums that consumers pay depend on their income and the price of the cheapest plan
Pijcons = Pj − (Pjmin + f (yi )). The price of uninsurance (j=0) is the mandate penalty, which
only depends on income Pi0 = Mi = My .
We used a logit model of insurance choice. The utility for consumer i of plan j is
uij = ũij + ij = (ξj,r,t + ξj,r,y ) − (αyi + αd ) · Pijcons + ij ,
j = 1, . . . J
ui0 = ũi0 + i0 = (β0 + βy + βr + βt + βd + σνi ) − (αy + αd ) · Mi + i0
Each individual choses the plan with the highest utility, which we denote ji∗
The plan qualities vary by region-year bins and region-income bins, ξij = ξj,r,t + ξj,r,y ; the
price sensitivity depends on consumers’ income, age, and gender, αi = αy + αd . In addition
to the fixed effects for each plan, we separately estimate the average cost of uninsurance.
In addition to allowing the value of insurance to vary with observable characteristics, we
want to capture the idea that the uninsured are likely to be people who, conditional on
observables, have low cost of uninsurance, so we allow for random coefficients in the value
of insurance: β(Zi , νi ) = β0 + βy + βr + βt + βd + σνi , with νi ∼ N (0, 1). This formulations
lets us flexibly match substitution patterns – including the key statistic of the elasticity of
insurance demand with respect to the mandate penalty. Let θ refer to all the parameters to
be estimated. The ’s are distributed i.i.d., type-I extreme value, which gives demand of
exp(ũij )
.
P (ji∗ = j|Zit , νi , θ) = PJ
exp(ũ
)
ik
k=0
19
Estimation
We estimate the model by simulated method of moments, incorporating micro moments
with an approach similar to Berry et al. (2004). We sample individuals from the CommCare
data and the uninsured in the ACS, adjusting for the fact that the ACS is only 1% of the
uninsured. For each individual ı̃ (with their associate Zı̃ ) we draw a νı̃ .
For each ξ we have a moment for the corresponding plan and group, g (either regionyear or region-income group) that matches the observed share of consumers in that group
who chose that plan, sObs
j , to the expected share given θ. If nsg is the number of sampled
individuals from group g, we have
1
Fj,g
(θ) = sObs
j,g −
1 X
P r(jı̃∗ = j|θ, Zı̃ , νı̃ .)
nsg ı̃∈g
For each β there is also a corresponding group, h – income, demographic, region, or year.
We use moments analogous to those above for the share of uninsured
G10,h (θ) = sObs
0,h −
1 X
P r(jı̃∗ = j|θ, Zı̃ , νı̃ ).
nsh ı̃∈h
We also match the covariance of plan premium and individual attributes. Following Berry
et al. (2004), we match
G2 (θ) =
X
j
1 X Cons
1 X Cons
Pij Zi {jiObs = j} −
P
Zı̃ P r(jı̃∗ = j|θ, Zı̃ , νı̃ )
n i
ns ı̃ ı̃j
!
Cons
= Mi . This helps us identify the different price-elasticity parameters.
where Pi,0
The final set of moments helps identify the variance of the random coefficients by matching the estimated insurance demand response from the natural experiments analyzed in
Section 3. If there is substantial heterogeneity in the value of insurance, the uninsured will
tend to be people with very low idiosyncratic values of insurance then an increase in the
mandate penalty will not increase their demand for insurance very much, since they were
not close to the margin of buying coverage. Thus, higher values of σ are likely to generate
less demand response to the mandate, and vice versa. For each experiment we match the
simulated change for the cheapest plan (in the corresponding year) to the change estimated
in Section 3:
G3 (θ) = (1 + ∆%DObs )
X
P r(jı̃∗ = jmin |Zı̃ , νı̃ , θ, MiP re ) −
ı̃
X
ı̃
20
P r(jı̃∗ = jmin |Zı̃ , νı̃ , θ, MiP ost )
We take extra sampling draws of people in this time period in order to minimize bias from
simulation error here.
Results
The results are summarized in in Table 5. The average price coefficient is -.044, and it does
not vary systematically with income, age or gender. There is a moderate average value of
uninsurance. Though one might expect this to be negative (positive value of insurance), it
needs to be positive to explain the fact that about 55% of the market is uninsured, despite
the substantial subsidies. Older people and women value insurance more. We also see that
CeltiCare and NHP were considered undesirable relative to BMC.
Table 5: Parameters in Demand Model
Average
Standard Error
Premium Coefficient
Change per income bin
Change per 5 year age bin
Change for Females
-0.044***
0.014
0.003
0.003
0.01585
0.00855
0.00286
0.00457
Uninsurance Dummy
Change per income bin
Change per 5 year age bin
Change for Females
0.44
-0.064
-0.127
-1.545
0.52653
0.62601
0.13296
1.44710
Plan Dummies (BMC= 0)
CeltiCare
Fallon
NHP
Network Health
-1.00**
0.315
-0.358***
0.009
0.40412
0.25684
0.11829
0.13361
Standard Deviation of
Value of Uninsurance
From Observables
From Unobserved (σ)
Total
1.4559
3.7690
4.04051
Note: This table reports the average demand parameters across individuals and how they differ with demographic characteristics. The plan dummies are standardized by setting the value of BMC to zero.
We allow the value of uninsurance to vary with observable and unobservables. Both
generate large variance in the value of uninsurance, but unobservables seem to play a larger
role, leading to a standard deviation of 1.5, when the total standard deviation is 4.
Because the logit parameters are hard to interpret, Table 6 gives the semi-elasticities
21
Table 6: Semi-Elasticities of Demand
% Change in Demand For:
$1 Increase in
Cost of:
Uninsurance
BMC HealthNet
CeltiCare
Fallon
NHP
Network Health
Uninsured
-0.72%
0.28%
0.05%
0.04%
0.13%
0.22%
BMC
0.91%
-2.48%
0.17%
0.06%
0.47%
0.87%
CeltiCare
Fallon
NHP
Network
Health
0.90%
0.96%
-3.78%
0.11%
0.87%
0.97%
0.86%
0.43%
0.14%
-3.20%
0.56%
1.24%
0.86%
0.94%
0.31%
0.15%
-3.27%
1.04%
0.89%
1.05%
0.21%
0.20%
0.63%
-2.96%
Note: Each cell reports the percent change in demand for the option in that column when the option in that
row raises its price by $1. Since we include the outside option in the market, each row sums to one when
the estimates are weighted by demand shares.
(the percentage change in demand for own and other options resulting from a $1 increase
in a price or penalty). The own-price elasticities are quite a bit higher than the (adjusted)
elasticities from Chan and Gruber (2010), but within the range found in the literature (see
?).
Table 7: Average Elasticities
2008
Avg. Own Price Semi-Elasticity
Semi-Elasticity of Any Insurance
w.r.t. Mandate Penalty
2009
2010
2011
-2.62% -2.65%
-3.13%
-3.12%
0.98%
0.95%
0.80%
0.90%
Note: These are the share weighted elasticities averaged across plans for each year. We allow the pricesensitivity parameters to vary by year and there are compositional changes in the demographics and plan
shares which contribute to the variation.
Table 7 show the average (share-weighted across plans) own-price elasticities and elasticity with respect to the mandate penalty. The own-price elasticity increases overtime. The
elasticity in 2008 with respect to the mandate penalty is very close to the .95% we estimated
in the reduced form analysis of the natural experiments.
22
4.2
Costs
To consider counterfactual pricing by firms, we need to estimate each firms cost of providing
insurance to a given consumer. The cost to plan j of insuring consumer i is
cij = exp(µZi + ψj + i ).
Individual expected cost are allowed to vary with all ex-ante observable characteristics. The
plans’ costs depends on their network which may vary differentially over time in different
regions.
We observe costs for all individuals in the CommCare market, but not individuals costs
when the are uninsured or otherwise-insured. To mitigate the bias from adverse selection
bias, we estimate the firm component of costs off a subsample of individuals who chose
different plans in different periods, using individual fixed-effects to partially control for unobserved selection. Table 8 shows the plan cost parameters broken down by before and after
2010, when Celticare entered the market. Prior to Celticare’s entry Neighborhood health
had the lowest costs. Other plans costs for treating the same patient ranged from 3% to 36%
higher. When Celticare entered it’s costs were 23% lower than Network Health’s.
Table 8: Plan Cost
Pre-2010
2010+
Network
Health
BMC
NHP
Fallon
CeltiCare
0%
0%
2.85%
4.31%
18.11%
17.03%
35.99%
59.20%
-22.85%
Note: The insurer fixed-effects are estimated from the subset of individuals who at some point enroll in
different plans. The parameters are estimated in a Poisson regression with individual fixed effects, the
reported percentages are exp ψj − 1, where Network Health’s ψj is set to zero.
We then divide observed costs by the corresponding exp(ψ)
ci = cij / exp(ψj,r,t )
and estimate the µ’s using the full sample
ci = exp(µZi + i ).
Table 9 and 10 summarize the estimated cost parameters. For every 5 years of age, costs
increase about 18% for males and 11% for females. On average costs for females are 6.4%
23
higher than males, but this ranges from 18% higher for 19-24 year olds down to 14% lower
for 60-64 year olds. All income groups have substantially lower (17-32% lower) costs than
the less than poverty group, but it does not vary systematically with income.
Table 9: Demographic Cost Parameters
Average
Male: 5 year age bin
Female: 5 year age bin
Female
17.59%
10.91%
6.42%
Max
Min
40.35% 9.09%
20.42% 2.46%
17.52% -13.65%
Note: The coefficients on individual demographics are estimated in a Poisson regression from the full sample
after removing the estimated firm component from the observed costs. The reported percentages are the
unweighted average/min/max of exp(µg − µc ) − 1, where g is an age×gender bin and the control group c is
the one lower age bin for lines 1 and 2 or males for line 3.
Table 10: Cost Parameters by Income Group
Percent of Federal Poverty Line
100-150 150-200 200-250 250-300
Relative to < Poverty
-24.94%
-17.49%
-26.28%
-31.71%
Note: The coefficients on income group (as the percent of the Federal Poverty Level) are estimated in a
Poisson regression from the full sample after removing the estimated firm component from the observed
costs. The reported percentages are exp µg − 1, when the µg for the Less than Poverty group is set to zero.
Since firms can only set one price, there may be adverse selection on both observables
and unobservables. Risk adjustment can mitigate or eliminate selection on observables. To
implement risk adjustment, the exchange estimates φi for each individual which indicates
how costly they are expected to be relative to the average enrollee. It then adjusts payments
accordingly so the expected profits that plan j earns from enrolling individual i are
E[πji ] = φi Pj − cij .
We cannot use the exact risk adjustment multipliers that the market used,23 so we con23
Ideally, we would use the same risk adjustment as the exchange (which incorporated diagnoses, etc.).
Unfortunately, the exchanges risk adjustment didnt start until 2010, and we are missing data for Q1-Q3 of
2010. Also, we dont have the counterfactual risk adjusters for the uninsured sample. Finally, since our cost
model is predicted only based on demographics, adding other factors like diagnoses would just increase noise
without improving the fit.
24
sider two possible types of risk adjustment. With perfect risk adjustment on demographics
ĉi = exp(Zi µ)
1 X
c̄ =
ĉi
ni i
ĉi
φi = .
c̄
So expected profits are φi (Pj − exp(ψj )c̄ · ε̄j ), where ε̄j = E[exp i |jj ∗ = j].
We also consider various levels of imperfect risk adjustment
φi (γ) = φγi
with γ ∈ [0, 1]. Perfect risk adjustment corresponds to γ = 1 and no risk adjustment corresponds to γ = 0. Even perfect risk adjustment cannot address selection on unobservables.
4.3
Simulations
We run counterfactuals to look at prices and quantities in the market under alternative
subsidy policies. Under a given subsidy policy, we can use the estimated demand and cost
parameters to calculate demand and profits for any vector of plan prices. We look for a Nash
Equilibrium, where insurers maximize profits
πj =
X
(φi · Pj − ĉj ci ) · qij (P Cons (P )),
i
where φi is the the risk adjustment score and ĉj comes from the cost model and demand
qij depends on the estimated parameters and consumer prices P Cons , which depend on the
subsidy policy and on the prices set by all firms.
Firm j’s first order condition is
1
Pj = m
φj
cj cm
j +
φ̄j
− Q1j
!
dQj
dPj
dQj −1 P
dqij
m
where cm
j ≡ dPj
i ci dPj is the (average) cost of plan j’s marginal consumers, φj (defined
P
analogously) is the (average) risk score for marginal consumers, and φ̄j ≡ Q1j i φi qij is the
average risk score for consumers of plan j.24 We use these first-order conditions as moments
dq
24
Since different types of individuals have different values of uninsurance, dPijj (and therefore cm
j and
m
φj ) can depend on how the subsidy is set. Note that under perfect risk adjustment (with no selection on
25
to find the pricing equilibrium in the market under each subsidy policy. Under price-linked
∂qij
dqij
∂qij
dq
∂qij
subsidies In this case dPj = ∂P Cons − ∂M . Under exogenous subsidies dPijj = ∂P Cons
. Since
j
j
m
cm
j , φj and φ̄j depend on the prices they will also vary across equilibria.
2009
In 2009 there were only 4 plans in the market. Network Health and BMC has fairly similar
costs. It is therefore not surprising that we find that under price-linked subsidies, the second
cheapest plan acts as an upper-bound for the cheapest plan. For a given level of the other
plan’s price, each plan’s first-order condition has a kink when it’s price equal’s the other
plan’s price, since below that level it’s price affects the subsidy and above it does not. This
generates a range of equilbria where BMC and Network health have the same price. Table 11
compares the highest-priced of these equilibria to the equilibrium under exogenous subsidies,
for the lowest-priced one, see Table 18 in the Appendix.
Table 11: 2009 Price-Linked and Exogenous Subsidies
In-Market Shares
BMC
Fallon
NHP
Network
Prices
PriceLinked
Exogenous
Diff
PriceLinked
Exogenous
Diff
46.7%
1.2%
9.6%
42.4%
43.3%
0.8%
5.4%
50.6%
-3.4%
-0.4%
-4.2%
8.2%
$392
$459
$420
$392
$383
$467
$426
$377
-$9
$8
$6
-$15
$395
$383
-$12
$187
$198
$12
Fraction
52.8%
48.1%
Uninsured
Cost per Insured Consumer
-4.7%
Cost per Eligible Consumer
Note: This is a comparison of the market equilibria under price-linked and exogenous subsidies. Since the
second cheapest plan acts as a bound on upper bound on the price for the cheapest plan under price-linked
subsidies, there are a range of equilibria, this shows the higher priced equilibrium. ‘In-Market Shares’ refers
to the share of individuals who purchase insurance (who are ∼ 40% of the market).
m
unobservables) φm
j = cj /c̄ so this becomes
Pj = cj c̄ +
c̄j
1
.
1 dQj
cm
j −
Qj dPj
Since the risk adjustment factor is multiplicative, with perfect risk adjustment firms make more profit from
individuals with a higher ci , so their markup is higher when marginal consumers are lower cost than the
average consumers, the opposite of what happens under adverse selection with no risk adjustment.
26
Table 12: 2009 Different Exogenous Subsidies
In-Market Shares
10% Lower
10% Higher
Subsidy
Baseline Subsidy
BMC
Fallon
NHP
Network
42.5%
0.8%
5.6%
51.1%
43.3%
0.8%
5.4%
50.6%
Fraction
63%
48.1%
Uninsured
Cost per Insured Consumer
43.4%
0.8%
5.5%
50.4%
Prices
10% Lower
Subsidy
Baseline
10% Higher
Subsidy
$385
$474
$430
$378
$383
$467
$426
$377
$384
$461
$423
$377
$385
$383
$383
$142
$199
$251
34.5%
Cost per Eligible Consumer
Note: This is a comparison of the market equilibria under different levels of the exogenous subsidies. The
baseline is the equilibrium subsidy under price-linked subsidies. The other columns show the equilibrium
under a subsidy that is 10% lower or 10% higher. ‘In-Market Shares’ refers to the share of individuals who
purchase insurance (who are ∼ 40% of the market).
Table 11 compares the highest priced of these equilibria to the equilibrium under exogenous subsidies. Prices for the cheaper plans are $9 and $15 dollars lower for BMC and
Network health. The other plans raise their prices under exogenous subsidies, because they
have much lower market share the average price per enrollee drops by $12. The lower prices
cause an additional 4.7% of customers to purchase insurance, so total spending per potential
enrollee actually increases under the exogenous subsidy. In the lower priced equilibrium, the
effects are qualitatively the same, but smaller; the cheapest price falls $7 and average price
paid is $4 lower, spending per potential enrollee is $4 higher.
The comparison to exogenous subsidies depend on the level at which the government
sets the subsidy. There is no reason to think that absent price-linked subsidies they would
hit that level exactly. Table 12 compares this baseline case to the market with exogenous
subsidies that are 10% higher or 10% lower. The prices and in-market shares do not change
much; not surprsingly, the fraction of uninsured drops substantially as the subsidies increase.
2011
In 2011 Celticare is the cheapest plan in the market and its costs are substantially (∼ 23%)
below the next cheapest plan. Because of this gap, the second cheapest plan (Network
Health) does not effectively cap the distortion in Celticare’s price under price-linked subsidies.
Table 13 shows the market shares and prices for both exogenous and price-linked subsidies.
27
Celticare’s price is $19 lower under exogenous subsidies. The distortion is larger than in
2009, despite the higher estimated price elasticities because the cost of the low-cost plan is
so much lower.
Table 13: 2011 Price-Linked and Exogenous Subsidies
In-Market Shares
NHP
Fallon
BMC
Network
Celticare
PriceLinked
Exogenous
5.0%
1.0%
14.7%
33.5%
45.8%
3.6%
0.7%
10.0%
25.0%
60.7%
Fraction
61.7%
58.1%
Uninsured
Cost per Insured Consumer
Prices
Diff
PriceLinked
Exogenous
Diff
-1.5%
-0.2%
-4.7%
-8.5%
14.9%
$546
$545
$508
$467
$424
$556
$553
$517
$465
$405
$10
$8
$9
-$1
-$19
$458
$438
-$20
$176
$183
$8
-3.5%
Cost per Eligible Consumer
Note: This is a comparison of the market equilibria under price-linked and exogenous subsidies. ‘In-Market
Shares’ refers to the share of individuals who purchase insurance (who are ∼ 40% of the market).
Network Health also lowers its price slightly under exogenous subsidies, but the other
plans increase their prices ( $7-$10). Since the two cheapest plans jointly start with 79% inmarket share, which increases to 86% after the price changes, the average price for insurance
goes down $20 or 3.7%. The fraction of the population that buys insurance goes up by 3.5
percentage points (9%), so spending per potential enrollee increases by $8 meaning total
spending in the market increases by 4.4%.
Comparison to reduced form estimates
Though still substantial, the price changes in the simulations are substantially smaller than
the $48 dollars estimated in Section 3. A large part of this difference can be explained by
the fact that the demand elasticities we estimate are substantially higher than those found
in Chan and Gruber (2010). If we plug the elasticities from Table 7 into Equation 5 we get
distortions of $19 for 2009 and $11 for 2011.
We suspect that there are some price important price interactions. When the cheapest
plan lowers its price it steals the price-sensitive consumers from the more expensive plans,
causing them to raise their price, which in turn feedback to amplify the effect of the distortion
on the cheapest plan. This is not captured in the reduced-form equation: in order to convert
28
the equivalent cost change into an estimated price increase, the reduced-form approach
assumes that a firm’s semi-elasticities are unaffected by other firms’ prices. That explains
why the simulation estimate for 2011 is substantially higher than the reduced form estimate.
The fact that the 2009 simulation estimate is lower, despite price feedback loop is evidence
of the importance of the second cheapest plan as a price cap during that time.
Welfare
The demand and cost parameters combined with the estimated prices and shares give us
total government subsidy costs and revenue from the mandate penalty, firm profits, and
consumer surplus for each subsidy policy. The other important component of welfare is
the externality of being uninsured. As a baseline, we use 80% of average healthcare costs.
(Estimates from Mahoney (2012) suggest that the uninsured only pay about 20% of their
medical bills.) Table 14 reports the different components of welfare in millions of dollars
per year. Since exogenous subsidies lower prices and lower uninsurance, they increase the
government’s subsidy costs and lower the mandate penalty revenue. The net effect is about
$9.06 million per year. Combined with a consumer surplus increase of $3.29 million and
a decrease in uncompensated care costs of $6.91 million, we get that the government and
consumers gain about $1.15 million. Firms on the other hand lose about $1.74 million per
year under exogenous subsidies relative to endogenous subsidies so the total welfare effect of
switching to exogenous subsidies is negative.
Table 14: Welfare under Price-Linked and Exogenous Subsidies
In Millions of Dollars per Year
PriceLinked Exogenous Difference
+
+
+
Government Subsidy Costs
Government Mandate Revenue
Net Government Costs
Consumer Surplus
Externality Savings
Consumer & Govt Welfare
Profits
Total Welfare
98.21
7.57
106.89
7.19
8.68
-0.38
90.64
41.94
66.42
99.7
45.23
73.33
9.06
3.29
6.91
17.72
14.44
18.86
12.7
1.15
-1.74
32.16
31.56
-0.6
Note: These numbers are based on the simulations for 2009. Externality saving per member month is equal
to 80% of the average monthly cost of health care for a consumer in the market
29
Finkelstein et al. (2015) suggest that uncompensated care costs are only 60% of average
health care costs. In that case the government and consumer portion of welfare drops to
being $.58 million per year higher under exogenous subsidies – all those additional people
brought into the market by low prices have such a low value for insurance that even when the
externality is included, it is not socially beneficial for them to buy insurance. When firms
losses are included, social surplus is then negative. If uncompensated care costs equal average
costs, then the government and consumers gain $2.88 million per year under exogenous
subsidies and the total welfare effect is also positive ($1.13 million/year).
These calculations do not include any health externalities of insurance, or direct benefits
that consumers may fail to take into account when making their decisions (‘internalities’).
We also do not attempt to include the paternalistic sentiment of valuing having health
insurance be affordable. Unless these benefits are substantial or the cost of uncompensated
care is high, these numbers suggest that separate from the subsidy structure, the government
may want to consider lowering subsidies (raising the affordable amount) because it is driving
people to buy insurance even when its value to them plus the value of the externality is less
than its cost.
5
Discussion
In this section, we discuss the policy implications of our results for different markets and
compare alternative subsidy structures.
5.1
Implications for Subsidized Insurance Markets
Given the available data, we believe that $20 is a reasonable estimate of the potential distortion of the endogenous subsidies in the Massachusetts CommCare market. However, a
couple caveats are in order. CommCare had additional price regulation rules in place, which
we do not model, which may have mitigated the effects of this distortion. We look at the
early years of the market; if the trend we see towards more elastic demand over time is
robust, it may become less of an issue. We also cannot be confident that pricing and entry
in the market had reached equilibrium. Increased competition (as we see with Celticare’s
entry) also mitigates the distortion.
The Massachusetts market has now been converted into an ACA exchange. These exchanges differ in several respects: plans of three generosity tiers, multi-plan insurers, subsidies that depend on the second cheapest silver plan, expansion to higher income groups,
inclusion of unsubsidized consumers. The unsubsidized consumers, estimated to be 20% of
30
the market, will mitigate the distortion if they do not all buy bronze level plans. In addition
medical loss ratios may be effective in limiting firms’ profit margins.
Other factors may exacerbate the distortion. A New York Times analysis found that 58%
of counties served by the federal exchange, have two or fewer insurers.25 While normally the
distortion is capped by the price of the third-cheapest silver plan, counties with one or two
insurers may not have a third-cheapest plan (or it may be controlled by the same insurer
as the second-cheapest). Multi-plan insurers may also face more of an incentive to distort
the price of a plan to raise the subsidy, because their other plans benefit from the increased
subsidy. While, we cannot estimate what the size of the distortion will be in the ACA
exchanges, our estimates suggest that it has the potential to be substantial and thus should
be an important policy consideration.
The magnitudes will differ, but this potential for distortion exists in any market where
(1) firms have some market power26 and (2) there is the possibility of substitution to an
unsubsidized outside option. Price-linked subsidies exacerbate existing market power by
effectively removing the competition of the outside option; they cause a larger distortion
when firms have more market power and the margin of substitution to the outside option is
more important.
Insurers in Medicare Advantage, Medicare Part D, and employer-sponsored insurance
programs all have market power and these markets have some substitution to an outside
option. In the Medicare Advantage market, which uses exogenous baseline subsidies,27 our
results suggest that switching to endogenous subsidies would create a pricing distortion unless
the subsidy was also applied to traditional Medicare (as in “premium support” proposals). If
the government does not care whether consumers use traditional Medicare or private plans,
price volatility of the outside option is not an issue in this case. In order to avoid the
potential for negative prices for traditional Medicare (if the Medicare Advantage bids are
high), a premium support system would need to count the cost of traditional Medicare as
another bid in the market.
Medicare Part D uses flat, price-linked subsidies (as in the ACA), but the distortion for
the main subsidy is probably relatively small (though the distortion from the low-income
subsidy is likely larger; see Decarolis (2013)). The subsidy is based on a national enrollment25
Moreover, about 20% of markets have just one insurer (Abelson et al. (2013). In theory, in single-insurer
markets the insurer could raise price arbitrarily without losing subsidized consumers. They will only be
limited by medical loss ratio requirements. These areas are disproportionately small and rural, but the
distortions there are potentially sizable.
26
The presence of market power is not a restrictive condition; it merely requires that a $1 price increase
does not cause a firm’s demand to fall to zero (as would be the case in perfect competition).
27
However, after applying this baseline subsidy, Medicare reduces the subsidy when a plan reduces its
price below the benchmark. This creates a different kind of pricing distortion, which may be significant.
31
weighted average of plan price bids. Because all plans’ prices affect the subsidy through this
average, our theoretical distortion applies to all plans – not just a subset of potentially pivotal
silver plans as in the ACA – but the distortion for each plan is smaller. It is approximately
proportional to the national market share of the plan’s parent insurer, the largest of which
is United Health Group with 28% in 2011 (see Decarolis, 2013).
Employers typically pick a small menu of options for their employees and set subsidies
based on prices (either implicitly or explicitly). To the extent that an employer’s chosen
insurer(s) have market power, this can lead to the same pricing distortion. Since tax rules
limit employers ability to subsidize employees’ outside options, employers who want to keep
prices down should strive to make their subsidies not depend, even implicitly, on insurers’
prices.
5.2
Comparing Subsidy Structures
We have so far discussed three subsidy alternatives:
1. price-linked subsidies with an exogenous mandate penalty (the current ACA policy),
2. price-linked subsidies also applied to the mandate penalty,
3. exogenous subsidies.
If insurers priced at cost, option 1 would have desirable properties; it would allow the government to simultaneously take on price risk, guarantee affordability for consumers, and ensure
a certain mandate penalty. Unfortunately, in imperfectly competitive markets, this policy
distorts pricing incentives – and our results suggest the distortion can be substantial.
Options 2 and 3 do not distort firm pricing, but cannot guarantee affordability. Exogenous subsidies and a fixed mandate penalty shift price risk onto poor enrollees and may,
if they grow too large, push post-subsidy prices to their lower bound of zero. Price-linked
subsidies applied to the mandate penalty create certainty about consumer prices, but shift
the volatility onto the mandate penalty. Note that both systems exogenously fix the total
incentive the government is offering to buy insurance – the subsidy plus the mandate penalty;
the systems differ only in whether the mandate penalty (and its contribution to the total
incentive) is fixed or allowed to vary.
To weigh the tradeoffs of endogenous and exogenous subsidies, consider the reasons why
the government subsidizes insurance and what it hopes to achieve by doing so. One reason
for the government to subsidize insurance is that there are substantial externalities to being
uninsured. The uninsured still receive healthcare and the government and hospitals pay
much of the costs; estimates from (Mahoney, 2012) suggest that the uninsured only pay for
32
about 20% of the care billed to them. Political rhetoric on subsidizing insurance tends to
focus on an alternative reason of wanting to make health insurance “affordable” for all.
If the primary concern is about externalities, then ideally the government would set
the total subsidy (subsidy plus mandate penalty) equal to the externality. However that
externality depends on the cost of health care and the government may not have a very good
estimate of what that will be. Since the prices insurers set depend on their costs, they could
be a good proxy for the externality. In that case the government might want to do a mix of
the current system of price-linked subsidies and exogenous total subsidy (with either fixed
or varying equilibrium mandate penalty). The better the estimate the government has of
expected costs, the more they will want to rely on the an exogenous subsidy which does not
distort pricing. The more competitive the market, the more the government will want to use
information on cost that comes from market prices because they can do without distorting
prices as much.
If affordability is the primary objective, that means that government is less concerned
with targeting the right total subsidy, and more concerned with preventing the cost uncertainty from translating into price uncertainty for consumers. If variance in the mandate
penalty is less politically concerning than variance in prices then our suggestion of applying
the subsidy to a higher initial penalty may be optimal. In general, the more competition
there is in the market the more the government can give consumers price stability because
doing so does not distort prices; the more certainty the government has about the cost of
healthcare, the more it will want exogenous subsidies because it is more able to get price
stability without distorting incentives.
Given that in many regions the ACA markets do not appear very competitive less reliance on endogenous subsidies may be optimal. The government may have reasonably good
estimates of costs from running Medicare or Medicaid, but the experience with Medicare
Advantage’s exogenous subsidies suggests that setting the exogenous subsidy appropriately
may still be challenging.
6
Conclusion
This paper considers the distortion of pricing incentives generated by price-linked subsidies
in health insurance exchanges, an important topic for economists analyzing these markets
and policy makers designing and regulating them. We highlight this distortion in a simple
theoretical model and derive sufficient statistics for estimating its size. We then use two natural experiments in the Massachusetts exchange to confirm that insurance demand responds
to the relative price of the outside option. Using the Massachusetts estimates to calibrate
33
a structural model of demand we find an upward distortion of the subsidy-pivotal cheapest
plan’s price of $22 per member-month, or 6% of the average price of insurance. The potential budgetary effect is substantial: Massachusetts had about 2 million member-months
of subsidized coverage in fiscal 2009, so a $22 increase in monthly subsidies would translate
to $44 million per year in government costs. For the ACA, using the CBO projection of 20
million subsidized enrollees annually, a $22 per month subsidy increase would translate to
$5.3 billion per year in federal spending.
We do not view these numbers as a precise estimate of either the historical distortion
in Massachusetts or the expected distortion in the ACA exchanges. Rather, we think that
our calibration shows that the pricing distortion we identify in theory should be of practical
concern. In addition to analyzing the ACA markets as data becomes available, we hope
future research will measure the relevant elasticities in Medicare Advantage, Medicare Part
D, and employer-sponsored insurance programs, to assess the importance of this pricing
distortion in those markets.
Endogenous prices have advantages. The right tradeoff between the pricing distortion on
the one hand and affordability and incentive concerns on the other depends on the level of
competition in the market and the precision of the regulator’s cost estimates; it will not be
the same for every market. We hope our analysis allows for a better understanding of the
tradeoffs involved.
34
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35
Appendix
A
Theory with Multi-Plan Insurers (ACA Case)
The distortion described above is exacerbated when firms offer multiple plans in a market.
In the ACA insurers must offer a plan in each of multiple tiers – bronze, silver, gold, and
platinum.28 Subsidies are set equal to the second-cheapest silver plan minus a pre-specified
“affordable” share of a consumer’s income.29 The fact that insurers are providing additional
plans provides an even greater incentive for an insurer to increase the price of its silver plan
because the higher subsidy increases demand for the insurer’s non-silver plans as well – again
by inducing more customers to enter the market.
Suppose each firm j offers plans in tiers l = 1, ..., L. The insurer maximizes profits:
X
(Pjl − cjl ) Qjl (P cons , M ) ,
max
Pj1 ...PjL
l
where Pjlcons = Pjl − S (P ) with S (P ) = P2nd,Silv − AffAmt. Following the same steps as
above, the first-order condition for the silver plan is:
X
dQjl
∂πj
(Pjl − cjl )
= Qjsilv (·) +
= 0.
∂Pjsilv
dPjsilv
l
The markup with exogenous subsidies is:
M kupEx
jsilv =
1
ηjsilv
+
1
X
∂Qjsilv
− ∂P cons
l6=silv
jsilv
(Pjl − cjl )
∂Qjl
cons
∂Pjsilv
The second term reflects the fact that the insurer captures revenue from consumers who
switch to its other plans when it raises the price of its silver plan. This is a standard effect
in settings with multi-product firms. However, with the subsidy set based on the second
cheapest silver plan, the markup for that subsidy-pivotal plan is:


P
M kupEnd
jsilv
l6=Silv
 ∂Qjl
(Pjl − cjl )  ∂P cons
1
=
+
ηjsilv − ηjsilv,M
jsilv

 ∂Qjsilv
−  ∂P cons
+
jsilv
∂Qjl

+

∂M
| {z }
Additional Distortion

.
∂Qjsilv
| ∂M
{z }
(7)


Additional Distortion
28
Platinum plans cover 90% of medical costs (comparable to a generous employer plan today); gold covers
80% of costs; silver covers 70% of costs; and bronze covers 60% of costs. Consumers with incomes below
250% of poverty also receive so called “cost-sharing subsidies” that raise the generosity of silver plans.
29
This subsidy is applied equally to all plans (with a cap ensuring that no premium is pushed below $0),
ensuring that at least two silver plans (and likely some bronze plans) cost less than the affordable amount
for low-income consumers.
36
The fact that other plans offered by the firms also gain some of the consumers driven into
the market by the additional subsidy generates an additional distortion.
How much larger the distortion is in the multi-product ACA case is not certain, and we
do not have data to credibly estimate its size. We discuss some of the issues in translating
our estimates for Massachusetts to the ACA case in Section 3.3.
B
Natural Experiments
This Section provides more details on the natural experiments we use and some robustness
checks.
B.1
Mandate Penalty Introduction
We estimate the effect through March 2008 for two reasons. First, the application process
for the market takes some time, so people who decided to sign up in January may not have
enrolled until March. Second, the mandate rules exempted from penalties individuals with
three or fewer months of uninsurance during the year, meaning that individuals who enrolled
in March avoided any penalties for 2008. However most of the effect is in December and
January, so focusing on those months does not substantially affect our estimates.
We collapse the data to the income group-month level and calculate the new enrollees in
the cheapest plan for each group and month, normalized by the same plan’s total enrollment
for the income group in June 2008 (as discussed above). The difference-in-differences model
we estimate is:
!
X
X
X
N ewEnrollg,t =
αg · 1g +
βm · 1{t = m} +
γg · 1g · 1{t = m}
g
g
m∈T
+
X
δg,t · 1g · Xt + εg,t ,
g,t
where 1g is an indicator for income group g, T is the set of months December 2007 through
March 2008, 1{t = m} is a dummy for the month of the observation begin m, and Xt is a
vector of time polynomials and CommCare-year dummies, the coefficients of which we allow
to vary across groups. The difference-in-difference coefficient of interest is γg for the groups
above 150% of poverty subject to the penalties.
Table 15 presents the regression results. Column (1) starts with a baseline singledifference specification that estimates based only on enrollment for the 150-300% poverty
group in December 2007-March 2008 relative to the surrounding months. Column (2) then
adds the <100% poverty group as a control group, to form the difference-in-difference estimates. Finally, Column (3) adds dummies for December-March in all years, forming the
triple difference that nets out general trends for those months in other years. All of these
specifications use data from March 2007 to June 2011 and also include CommCare-year dummies and time polynomials separately for the treatment and control groups.30 Despite the
30
CommCare plan years run from July to June, so the year dummies are stable over the treatment period
37
Table 15: Introduction of the Mandate Penalty.
Dependent Var: New Enrollees in Cheapest Plan / June 2008 Enrollment
Variable
(1)
(2)
(3)
Sum of Dec2007 - Mar2008
coefficients (below)
0.253***
(0.017)
0.237***
(0.023)
0.225***
(0.024)
150-300% Poverty x Dec2007
0.112***
(0.003)
0.073***
(0.004)
0.043***
(0.005)
0.025***
(0.006)
0.110***
(0.006)
0.067***
(0.006)
0.033***
(0.006)
0.027***
(0.006)
0.103***
(0.007)
0.069***
(0.006)
0.033***
(0.006)
0.020***
(0.007)
x Jan2008
x Feb2008
x Mar2008
Control Group (<100% Poverty)
X
Triple Difference (dummies for
Dec-March)
Observations
51
102
R-Squared
0.969
0.923
Robust standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1
X
X
102
0.925
NOTE: This table performs the difference-in-difference regressions analogous to the graphs in Figure 1. The
dependent variable is the number of new CommCare enrollees who choose the cheapest plan in each month
in an income group, scaled by total group enrollment in that plan in June 2008. There is one observation
per income group (the 150-300% poverty treatment group, plus the <100% poverty control group in columns
(2) and (3)) and month (from April 2007 to June 2011). All specifications include CommCare-year dummy
variables and fifth-order time polynomials, separately for the treatment and control group, to control for
underlying enrollment trends. (The CommCare-year starts in July, so these dummies will not conflict with
the treatment months of December to March.) Specification (3) also includes dummy variables for all calendar
months of December-March for the treatment group, to perform the triple-difference. See the note to Figure
1 for the definition of new enrollees and the cheapest plan.
small number of group-month observations, all the relevant coefficients are highly significant.
Summing across treatment months, the total excess enrollment after the mandate penalty
introduction was between 22-25% of equilibrium market size. Table 2 takes the final, tripledifference specification from Table 15 and breaks the analysis down into narrower income
groups (by 50% of poverty interval, the narrowest we have).
We would like to interpret the increases in enrollment as being the result of the $17.50–
$52.50 monthly mandate penalty that went into effect in January 2008. However, the 2007
uninsurance penalty of $219 was assessed based on coverage status in December 2007,31
from December 2007 to March 2008. We use data only up to June 2011 because of significant changes in the
prices and availability of the cheapest plans that took effect in July 2011.
31
In addition, an exemption was given for individuals who applied for CommCare in 2007 and enrolled on
38
Share Exiting
.2
0
0
.1
.02
Share Exiting
.04
.3
.06
.4
.08
making that month’s effective penalty much larger. If consumers were only buying insurance
because of the larger December penalty, we would expect many of them to leave the market
soon after the monthly penalty dropped to the lower level. To assess this story, Figures
3a and 3b plot the probability of market exit within 1 and 6 months, respectively, for new
enrollees. Each point represents a distinct group of new enrollees in the corresponding month
shown on the x-axis, and the y-axis value is the share who exited within 1 or 6 months. While
there is a general upward trend over time, there is no jump in either series for people who
joined in December 2007. The large spike for people enrolling in March 2008 is due to an
unrelated income verification program.32 This analysis suggests that consumers were not
enrolling for just December to avoid the $219 penalty and leaving soon after because of the
lower penalty.
June2007
Dec2007
June2008
Month of Initial Enrollment
150−300% Poverty
Dec2008
June2007
<100% Poverty
Dec2007
June2008
Month of Initial Enrollment
150−300% Poverty
(a) One Month
Dec2008
<100% Poverty
(b) Six Months
Figure 3: Share of New Enrollees Exiting Within the Specified Number of Months.
NOTE: These graphs show the rate of exiting CommCare coverage within one month (left figure) and six
months (right) of initial enrollment among people newly enrolling CommCare in a given month. If individuals
had enrolled at the end of 2007 to avoid the one-time $219 penalty and quickly dropped coverage thereafter,
we would expect to see a spike for the 150-300% poverty series in December 2007 and/or January 2008. The
absence of such a spike in exits suggests that the monthly penalties starting in January 2008 were sufficient
to induce individuals to remain in the program. The spike that does occur among new enrollees in March
2008 reflects the start of an income-verification program for the 150-300% poverty group in April 2008. See
the note to Figure 1 for the definition of new enrollees and the cheapest plan.
January 1, 2008. However, December 31, 2007, was the main advertised date for assessing coverage status.
32
The income verification program took effect in April 2008 for individuals above 150% of poverty (but
earlier on for people < 100% poverty). Prior to April, income group at enrollment was based partly on
self-reporting, and changes in income over time were also supposed to be self-reported. The verification
program uncovered a large number of ineligible people, who were dis-enrolled in April 2008 and subsequent
months. This event can also explain the upward trend in exits within 6 months leading up to April 2008.
39
B.2
Affordable Amount Decrease Experiment
This approach addresses a concern with our first method: that the introduction of a mandate penalty may have a larger effect (per dollar of penalty) than a marginal increase in
penalties.Some individuals may obtain coverage to avoid the stigma of paying a penalty, but
this stigma might not change when mandate penalties increase. An argument against the
stigma explanation is that the legal mandate to obtain insurance had been in place since July
2007, though without financial enforcement. In addition, individuals below 100% of poverty
were also required to obtain insurance (again without financial enforcement). However to
the extent there is a stigma specifically from paying a fine for non-coverage, this concern is
valid.
The most significant changes in the affordable amount occurred in July 2007 for consumers between 100-150% of poverty. Prices in CommCare usually change in July, but in
the first year of the program, prices were held fixed from November 2006 to June 2008, so
firms’ price-bids did not change at the same time as this change in the affordable amount.
For the first half of 2007, their affordable amount was $18 and premiums ranged from $18
for the cheapest plan to $74.22 for the most expensive. In July 2007, CommCare eliminated
premiums for this group, so all plans became free. We can think of this as the combination
of two effects: (1) The affordable amount was lowered from $18 to zero, and (2) the premium
of all plans besides the cheapest one were differentially lowered to equal the cheapest premium (now $0). The second change should unambiguously lower enrollment in what was the
cheapest plan, since the relative price of all other plans falls. Therefore, if we use the actual
policy change to estimate the effect on new enrollment in the (formerly) cheapest plan, this
will be a lower bound on the effect of just lowering the affordable amount (the effect we want
to estimate).
As a control group, we use the 200-300% poverty group, whose affordable amounts were
essentially unchanged in July 2007. The affordable amount for consumers 200-250% poverty
was unchanged at $70, while the amount for 250-300% poverty was lowered by just $1 from
$106 to $105. To the extent this slightly increased enrollment for the control group, it
would only bias our estimates downward. We exclude other incomes from our controls for
several reasons. First, we do not use the below 100% poverty group because of its somewhat
different enrollment history and trends. Whereas the groups above poverty only started
joining CommCare in February 2007, the below 100% poverty group became eligible in
November 2006 and had a large influx in early 2007 due to an auto-enrollment. Second, we
exclude the 150-200% of poverty group from the controls because their affordable amount also
fell non-trivially (from $40 to $35) in July 2007. While this smaller change does not produce
as dramatic of an enrollment spike, we show in Appendix B.3 that their enrollment increase
was consistent with semi-elasticity calculated from the the mandate penalty introduction
results presented in Table 2.
Table 16 presents the regression results corresponding to Figure 2. Again, in Column
(1) we just look at the enrollment difference for the 100-150% poverty treatment group
relative to trend, captured by CommCare-year dummies and time polynomials. Column (2)
then adds the 200-300% poverty control group to form the difference-in-difference estimates.
The last column does a triple-difference, further netting out changes in July-October of
other years. The coefficients change a bit more between specifications, but they all imply
40
Table 16: Decrease in the Affordable Amount.
Dependent Var: New Enrollees in Cheapest Plan / June 2008 Enrollment
Variable
(1)
(2)
(3)
Sum of July - Oct 2007
coefficients (below)
0.200***
(0.021)
0.156***
(0.031)
0.169***
(0.032)
100-150% Poverty x July2007
0.064***
(0.005)
0.052***
(0.005)
0.022***
(0.005)
0.062***
(0.005)
0.060***
(0.008)
0.031***
(0.008)
0.011
(0.008)
0.054***
(0.008)
0.063***
(0.008)
0.035***
(0.009)
0.016*
(0.008)
0.055***
(0.008)
x Aug2007
x Sep2007
x Oct2007
Control Group (200-300% poverty)
X
Triple Difference (dummies for
July - October)
Observations
52
104
R-Squared
0.988
0.981
Robust standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1
X
X
104
0.981
NOTE: This table performs the difference-in-difference regressions analogous to the graphs in Figure ??,
with specifications analogous to those in Table 15. The dependent variable is the number of new CommCare
enrollees who chose the cheapest plan in each month in an income group, scaled by total group enrollment in
that plan in June 2008. There is one observation per income group (the 100-150% poverty treatment group,
and the 200-300% poverty control group in columns (2) and (3)) and month (from March 2007 to June 2011).
All specifications include CommCare-year dummy variables and fifth-order time polynomials, separately for
the treatment and control group, to control for underlying enrollment trends. (The first CommCare year ends
in June 2008, so there is no conflict between the CommCare-year dummies and the treatment months of July
to October 2007.) Specification (3) also includes dummy variables for all calendar months of July-October for
the treatment group, to perform the triple-difference. Where applicable, specifications also include dummy
variables to control for two unrelated enrollment changes: (a) for 100-150% poverty in December 2007, when
there was a large auto-enrollment spike, and (b) for 200-300% poverty in each month from December 2007
to March 2008, when there was a spike due to the introduction of the mandate penalty. See the note to
Figure ?? for the definition of new enrollees and the cheapest plan.
significant enrollment increases of at least 15 percentage points. Table 3 presents just the
triple-difference, our preferred specification.
B.3
Robustness Check
We use the smaller changes in the affordable amount that occurred for the 150-200% poverty
group in July 2007 as a check on the semi-elasticity estimated for this group. Table 17 shows
41
the results. Our preferred triple-difference estimate from column (3), indicates that the $5
affordable amount decrease translated into a 6.3% increase in demand for the cheapest plan.
This implies a semi-elasticity of 0.0126, quite similar to the semi-elasticity of 0.0119 that we
found for this group using the mandate penalty introduction (see Table 4).
Table 17: Decrease in the Affordable Amount: 150-200% Poverty
Dependent Var: New Enrollees in Cheapest Plan / June 2008 Enrollment
Variable
(1)
(2)
(3)
Sum of July - Oct 2007
coefficients (below)
0.063***
(0.019)
0.052**
(0.025)
0.063**
(0.027)
150-200% Poverty x July2007
0.013***
(0.005)
0.029***
(0.005)
0.013**
(0.005)
0.008
(0.005)
0.017**
(0.007)
0.016**
(0.007)
0.011*
(0.006)
0.009
(0.006)
0.018**
(0.008)
0.022***
(0.008)
0.015**
(0.007)
0.009
(0.006)
x Aug2007
x Sep2007
x Oct2007
Control Group (200-300% poverty)
X
Triple Difference (dummies for
July - October)
Observations
52
104
R-Squared
0.960
0.957
Robust standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1
X
X
104
0.958
NOTE: This table performs the difference-in-difference regressions analogous to those in Table 3 (see the
note to that table for additional information), but with a treatment group of enrollees 150-200% poverty,
whose affordable amount dropped from $40 to $35 in June 2008. The control group continues to be enrollees
200-300% poverty, whose affordable amounts were essentially unchanged at that time.
C
Simulations
In 2009 the two cheapest plans set the same price, so there were a range of equilibria under
price-linked subsidies. Table 18 shows the lower priced equilibrium and compares it to the
equilibrium under exogenous subsidies.
42
Table 18: 2009 Price-Linked and Exogenous Subsidies
In-Market Shares
BMC
Fallon
NHP
Network
PriceLinked
Exogenous
48.2%
0.9%
6.7%
44.2%
43.3%
0.8%
5.4%
50.6%
Fraction
53.1%
51.7%
Uninsured
Cost per Insured Consumer
Prices
Diff
PriceLinked
Exogenous
Diff
-4.9%
-0.1%
-1.3%
6.4%
$384
$465
$423
$384
$384
$468
$426
$377
$0
$3
$3
-$7
$387
$384
-$4
$181
$186
$4
-1.4%
Cost per Eligible Consumer
Note: This is a comparison of the market equilibria under price-linked and exogenous subsidies. Each
equilibrium is calculated using the demand and cost structures estimated above and the first-order condition
for firms, which varies by subsidy structure. Since the second cheapest plan acts as a bound on upper bound
on the price for the cheapest plan under price-linked subsidies, there are a range of equilibria, this shows the
lower priced equilibrium. ‘In-Market Shares’ refers to the share of individuals who purchase insurance (who
are ∼ 40% of the market).
43